Diana, Yoko, Kathy and Nora jointly contributed to the cost of a present for their sister. Diana's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Nora's contribution to the total of Yoko's and Kathy's contribution is 3 : 2. What is the total contribution by the four girls if Yoko's contribution is ¹₃ of Kathy's contribution and the total amount contributed by Diana and Nora is $96?

Diana	Yoko	Kathy	Nora	Total
1x10	1x10			2x10
	2x2		3x2
	1x1	3x1
10 u	1 u	3 u	6 u	20 u

Working backwards.

Total amount that Yoko and Kathy had is the combined repeated identity.
LCM of 2 and 4 = 4

Total amount that Yoko, Kathy and Nora had is the next combined repeated identity.
LCM of 1 and 10 = 10 

Total amount contributed by Diana and Nora
= 10 u + 6 u
= 16 u

16 u = 96

2 u = 96 ÷ 16 = $6

Total contribution by the four girls
= 20 u
= 20 x 6
= $120

Answer(s): $120